Question: $\dfrac{ 3w + 3x }{ 7 } = \dfrac{ -4w + 7y }{ -3 }$ Solve for $w$.
Multiply both sides by the left denominator. $\dfrac{ 3w + 3x }{ {7} } = \dfrac{ -4w + 7y }{ -3 }$ ${7} \cdot \dfrac{ 3w + 3x }{ {7} } = {7} \cdot \dfrac{ -4w + 7y }{ -3 }$ $3w + 3x = {7} \cdot \dfrac { -4w + 7y }{ -3 }$ Multiply both sides by the right denominator. $3w + 3x = 7 \cdot \dfrac{ -4w + 7y }{ -{3} }$ $-{3} \cdot \left( 3w + 3x \right) = -{3} \cdot 7 \cdot \dfrac{ -4w + 7y }{ -{3} }$ $-{3} \cdot \left( 3w + 3x \right) = 7 \cdot \left( -4w + 7y \right)$ Distribute both sides $-{3} \cdot \left( 3w + 3x \right) = {7} \cdot \left( -4w + 7y \right)$ $-{9}w - {9}x = -{28}w + {49}y$ Combine $w$ terms on the left. $-{9w} - 9x = -{28w} + 49y$ ${19w} - 9x = 49y$ Move the $x$ term to the right. $19w - {9x} = 49y$ $19w = 49y + {9x}$ Isolate $w$ by dividing both sides by its coefficient. ${19}w = 49y + 9x$ $w = \dfrac{ 49y + 9x }{ {19} }$